mutualinf: An R Package for Computing and Decomposing the Mutual Information Index of Segregation

School of Computer Science

Department of Sociology

Department of Economics

Department of Computer Science

Abstract

In this article, we present the R package mutualinf for computing and decomposing the mutual information index of segregation by means of recursion and parallelization techniques. The mutual information index is the only multigroup index of segregation that satisfies strong decomposability properties, both for organizational units and groups. The mutualinf package contributes by (1) implementing the decomposition of the mutual information index into a “between” and a “within” term; (2) computing, in a single call, a chain of decompositions that involve one “between” term and several “within” terms; (3) providing the contributions of the variables that define the groups or the organizational units to the overall segregation; and (4) providing the demographic weights and local indexes employed in the computation of the “within” term. We illustrate the use of mutualinf using Chilean school enrollment data. With these data, we study socioeconomic and ethnic segregation in schools.

Akerlof, George, and Rachel E. Kranton. 2010. Identity Economics How Our Identities Shape Our Work, Wages and Well-Being. Princeton University Press.

Crenshaw, Kimberle. 1990. “Mapping the Margins: Intersectionality, Identity Politics, and Violence Against Women of Color.” Stan. L. Rev. 43: 1241.

Dowle, Matt, and Arun Srinivasan. 2021. Data.table: Extension of ‘Data.frame‘. https://CRAN.R-project.org/package=data.table.

Duncan, Otis Dudley, and Beverly Duncan. 1955. “A Methodological Analysis of Segregation Indexes.” American Sociological Review 20 (2): 210.

Elbers, Benjamin. 2021. Segregation: Entropy-Based Segregation Indices. https://CRAN.R-project.org/package=segregation.

Flückiger, Yves, and Jacques Silber. 1999. The Measurement of Segregation in the Labor Force. Physica-Verlag Heidelberg.

Frankel, David M., and Oscar Volij. 2011. “Measuring School Segregation.” Journal of Economic Theory 146 (1): 1–38.

Guinea-Martin, Daniel, and Ricardo Mora. 2021. “Computing Decomposable Multigroup Indexes of Segregation.” Universidad Carlos III de Madrid. Departamento de Economía.

Kullback, Solomon. 1959. Information Theory and Statistics. Wiley Publication in Mathematical Statistics.

Massey, D. S., and N. A. Denton. 1988. “The Dimensions of Residential Segregation.” Social Forces 67 (2): 281–315.

Mora, Ricardo, and Javier Ruiz-Castillo. 2003. “Additively Decomposable Segregation Indexes. The Case of Gender Segregation by Occupations and Human Capital Levels in Spain.” The Journal of Economic Inequality 1 (2): 147–79.

———. 2011. “Entropy-Based Segregation Indices.” Sociological Methodology 41 (1): 159–94.

Reardon, Sean F, and Glenn Firebaugh. 2002. “Measures of Multigroup Segregation.” Sociological Methodology 32 (1): 33–67.

Theil, Henri, and Anthony J. Finizza. 1971. “A Note on the Measurement of Racial Integration of Schools by Means of Informational Concepts.” The Journal of Mathematical Sociology 1 (2): 187–93.

Zoloth, Barbara S. 1974. An Investigation of Alternative Measures of School Segregation. University of Wisconsin.